Output Regulation Of Uncertain Nonlinear Systems And Its Application

The problem of nonlinear output regulation is one of the most important issues inthe control theory and its application, which involves nonlinear stabilizaion, tracking ref-erence control and disturbance rejection as special cases. The objective of the output reg-ulation is to design a feedback control law to achieve tracking a class of reference inputand rejecting in the presence of a class of disturbances while maintaining the closed-loopsystem overall signals uniform ultimate boundedness. When the reference input and theexpected disturbances are generated by autonomous diferential equation which is calledthe exosystem, the problem is also called servomechanism problem.In this thesis, the problems with non-parametric uncertain nonlinear systems areconsidered. Firstly the stabilization problem is investigated for diferent uncertain nonlin-ear systems for example, with known state variables, with partly known state variables orwith time delay. Then output regulation problem is addressed, and the result is applied toa tracking control problem associated with micro spacecraft. The main contributions aresummarized as follows:1. The stabilization problem of uncertain nonlinear systems is studied as a specialcase of the output regulation problem. First of all, the global stabilization problem foruncertain nonlinear systems with odd integer in lower triangular form is solved, underthe assumption that the state variables are known, with a non-lipschitz continuous statefeedback control designed by using finite-time stability theorem and non-smooth feed-back design. Then an adaptive fuzzy output feedback backstepping control method isdeveloped for a class of nonlinear pure-feedback systems whose state variables are notdirectly available. Fuzzy logic systems are introduced to approximate the unknown non-linear functions. The filtered signals are utilized to solve the algebraic loop problemsencountered in the implementation of the usual controllers. An adaptive fuzzy control isproposed using generized observer and Lyapunove stability theorem. At last the problemof global output feedback stabilization for a glass of upper-triangular nonlinear systemswith time-delay in the state is considered. The delay-independent output feedback con-troller is proved to be exist based on extended homogeneous domination approach andlow gain observer. 2. When the state variables are available for feedback, the output regulation prob-lem for uncertain nonlinear systems driven by linear exosystems is investigated. Theuncertainties are supposed to be bounded by known functions. Firstly a linear internal isdesigned and a dynamic smooth state feedback control is proposed by making use of theinternal model. Then we apply nonsmooth analysis theory to backstepping method foravoiding the restriction that the virtual controls must be smooth functions. We introducethe error internal model and utilize exosystem information to stabilize feedback inputitems. A nonsmooth state feedback control is prosposed to solve the output regulationproblem.3. The output regulation problem for uncertain nonlinear systems where the statevariables are not always available is addressed. We focus on the nonlinear systems withdynamic uncertaity and nonlinear exosystem. K-filters are designed to estimate the un-measured states.A fuzzy output feedback control is proposed by using linear internal.Using the designed high-gain observer of state estimation, and combining the fuzzy adap-tive control with backstepping approach, an adaptive control fuzzy backstepping controlscheme is obtained for a class of SISO uncertain system with nonlinear exosystem.4. The output regulation problem with time delay uncertain nonlinear systems driv-en linear exosystem is studied. At the backstepping frame, using appropriate Lyapunov-Krasovskii functional, an adaptive fuzzy output feedback control is developed by com-bining fuzzy observer and internal model.5. Some results of output regulation problem are applied to solve the problem ofattitude tracking and disturbance rejection. The complexity of the question is in that thesystems contains the uncertain element and the disturbance contained by the exosystem.A linear internal model with parametric uncertainty is designed utilizing the immersiontechnique. By combining adaptive control theory and Lyapunov theory, state feedbackcontrollers to deal with the uncertainty of the systems and the parametric uncertainty ofthe exosystem are designed.